Problem: Luis is 20 years older than Umaima. Seventeen years ago, Luis was 3 times as old as Umaima. How old is Umaima now?
Solution: We can use the given information to write down two equations that describe the ages of Luis and Umaima. Let Luis's current age be $l$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $l = u + 20$ Seventeen years ago, Luis was $l - 17$ years old, and Umaima was $u - 17$ years old. The information in the second sentence can be expressed in the following equation: $l - 17 = 3(u - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = u + 20$ . Substituting this into our second equation, we get the equation: $(u + 20)$ $-$ $17 = 3(u - 17)$ which combines the information about $u$ from both of our original equations. Simplifying both sides of this equation, we get: $u + 3 = 3 u - 51$ Solving for $u$ , we get: $2 u = 54$ $u = 27$.